Finite Group Databasebeta

← #116080

Subgroups — #116080

Order 512.

623 conjugacy classes of subgroups.

The subgroup lattice has 399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21332C211yesmaximal, characteristic
2#20755C211yesmaximal, characteristic
3#17486C211yesmaximal, characteristic
4C2×#1481C211yesmaximal, characteristic
5#8095C211yesmaximal, characteristic
6#7924C211yesmaximal, characteristic
7#7893C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C22×C4⋊C8C2211yescharacteristic
13#2285C2211yescharacteristic
14C4×#117C2211yescharacteristic
15#1996—22no—
16#1996C414yes—
17#1832—22no—
18#1831—22no—
19#1740—22no—
20#1729—22no—
21#1493—22no—
22#1487—22no—
23#1481—22no—
24#1481—22no—
25#1481—22no—
26C2×Q8⋊C8—22no—
27#1303—22no—
28#1282—22no—
29#1279—22no—
30C22×M16—21no—
31C23×C8—21no—
32#533—21no—
33#533—21no—
34#533—21no—
35#533—21no—
36#533—21no—
37#533—21no—
38#533—21no—
39#533—21no—
40C2×C4⋊Q8Q811yescharacteristic
41C2×C4⋊Q8Q811yescharacteristic
42C2×#125—21no—
43C2×C22⋊Q8—21no—
44C2×C22⋊Q8C2×C412yes—
45C2×C4×Q8—21no—
46C2×C4×Q8D412yes—
47C2×#117—21no—
48C2×#117—21no—
49C2×#117D412yes—
50C22×C42C2311yescharacteristic
51#431—21no—
52#431—21no—
53#431—21no—
54#431—21no—
55#431—21no—
56#431—21no—
57#431—21no—
58#431D412yes—
59#423—21no—
60#423—21no—
61#423—21no—
62#423—21no—
63C2×C4⋊C8—21no—
64C2×C4⋊C8—21no—
65C2×C4⋊C8—21no—
66C2×C4⋊C8—21no—
67C2×C4⋊C8—21no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8—21no—
70C2×C4⋊C8—21no—
71C2×C4⋊C8D412yes—
72C2×C4⋊C8D412yes—
73C2×C22⋊C8—21no—
74C2×C22⋊C8—21no—
75C2×C4×C8—21no—
76C2×C4×C8D412yes—
77#384—21no—
78#382—21no—
79#380—21no—
80#380C2×C412yes—
81C4×C4⋊C4—21no—
82C4×C4⋊C4—21no—
83C4×C4⋊C4—21no—
84C4×C4⋊C4—21no—
85C4×C22⋊C4C2×C412yes—
86C4×C22⋊C4D412yes—
87#376—21no—
88C43—21no—
89#342—28no—
90#336—28no—
91Q8⋊C8—28no—
92Q8⋊C8—28no—
93C22×Q8—21no—
94C22×Q8C4⋊C412yes—
95C23×C4C22×C411yescharacteristic
96C23×C4C2×D411yescharacteristic
97C23×C4C2×D411yescharacteristic
98C2×M16—41no—
99C2×M16—41no—
100C2×M16—42no—
101C2×M16—42no—
102C22×C8—22no—
103C22×C8—22no—
104C22×C8—22no—
105C22×C8—41no—
106C22×C8—41no—
107C22×C8—41no—
108C22×C8—42no—
109C22×C8—42no—
110C4⋊Q8—21no—
111C4⋊Q8—21no—
112C4⋊Q8—21no—
113C4⋊Q8—21no—
114C4⋊Q8—21no—
115C4⋊Q8—21no—
116C4⋊Q8—21no—
117C4⋊Q8—21no—
118#125—41no—
119#125—41no—
120#125—41no—
121#125—41no—
122C22⋊Q8—22no—
123C22⋊Q8—22no—
124C22⋊Q8—22no—
125C22⋊Q8—22no—
126C22⋊Q8—41no—
127C22⋊Q8—41no—
128C22⋊Q8—41no—
129C22⋊Q8—41no—
130C4×Q8—22no—
131C4×Q8—22no—
132C4×Q8—22no—
133C4×Q8—22no—
134C4×Q8—41no—
135C4×Q8—41no—
136C4×Q8—41no—
137C4×Q8—41no—
138#117—22no—
139#117—22no—
140#117—22no—
141#117—22no—
142#117—41no—
143#117—41no—
144#117—41no—
145#117—41no—
146#117—42no—
147#117—42no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4—41no—
157C2×C4⋊C4C4⋊C412yes—
158C2×C22⋊C4—22no—
159C2×C22⋊C4—22no—
160C2×C22⋊C4C22⋊C414yes—
161C2×C42—22no—
162C2×C42—22no—
163C2×C42—22no—
164C2×C42—22no—
165C2×C42—41no—
166C2×C42C2×D411yescharacteristic
167C2×C42C2×D411yescharacteristic
168C2×C42C2×D411yescharacteristic
169C2×C42C2×D411yescharacteristic
170C2×C42C2×D411yescharacteristic
171C2×C42C2×Q811yescharacteristic
172C2×C42#4111yescharacteristic
173C2×C42#4111yescharacteristic
174C2×C42#4111yescharacteristic
175C2×C42#4111yescharacteristic
176C2×C42#4111yescharacteristic
177C2×C42#4111yescharacteristic
178C4⋊C8—22no—
179C4⋊C8—22no—
180C4⋊C8—22no—
181C4⋊C8—22no—
182C4⋊C8—22no—
183C4⋊C8—41no—
184C4⋊C8—41no—
185C4⋊C8—41no—
186C4⋊C8—41no—
187C4⋊C8—41no—
188C4⋊C8—41no—
189C4⋊C8—41no—
190C22⋊C8—22no—
191C22⋊C8—41no—
192C22⋊C8—41no—
193C22⋊C8—41no—
194C4×C8—22no—
195C4×C8—22no—
196C4×C8—22no—
197C4×C8—41no—
198#95—22no—
199#95—22no—
200#95—22no—
201#95—41no—
202C24C2×C22⋊C411yescharacteristic
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8—44no—
206C2×Q8—41no—
207C2×Q8—41no—
208C2×Q8—82no—
209C22×C4—24no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—81no—
215C22×C4C2×C4⋊C411yescharacteristic
216C22×C4#11711yescharacteristic
217C22×C4C4×D411yescharacteristic
218C22×C4C4×D411yescharacteristic
219C22×C4C4×D411yescharacteristic
220C22×C4C4×D411yescharacteristic
221C22×C4#12011yescharacteristic
222C22×C4#12111yescharacteristic
223C22×C4#12111yescharacteristic
224C22×C4#12111yescharacteristic
225C22×C4#12111yescharacteristic
226C22×C4#12111yescharacteristic
227C22×C4#12111yescharacteristic
228C22×C4C22⋊Q811yescharacteristic
229C22×C4C22⋊Q811yescharacteristic
230C22×C4#12311yescharacteristic
231C22×C4#12411yescharacteristic
232C22×C4#12711yescharacteristic
233C22×C4#13512yes—
234C22×C4#13512yes—
235C22×C4#13712yes—
236C22×C4#13712yes—
237M16—82no—
238M16—81no—
239M16—81no—
240C2×C8—42no—
241C2×C8—42no—
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—44no—
245C2×C8—44no—
246C2×C8—82no—
247C2×C8—82no—
248C2×C8—81no—
249C2×C8—81no—
250C2×C8—82no—
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—44no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—42no—
265C4⋊C4—42no—
266C4⋊C4—82no—
267C4⋊C4—82no—
268C22⋊C4—24no—
269C22⋊C4—24no—
270C22⋊C4—42no—
271C22⋊C4—42no—
272C22⋊C4—44no—
273C42—44no—
274C42—42no—
275C42—42no—
276C42—42no—
277C42—42no—
278C42—82no—
279C42—81no—
280C42—81no—
281C42#12011yescharacteristic
282C42#12011yescharacteristic
283C42#12111yescharacteristic
284C42#12111yescharacteristic
285C42C22⋊Q811yescharacteristic
286C42C22⋊Q811yescharacteristic
287C42C22⋊Q811yescharacteristic
288C42C22⋊Q811yescharacteristic
289C42#12311yescharacteristic
290C42#12311yescharacteristic
291C42#12311yescharacteristic
292C42#12311yescharacteristic
293C42#12411yescharacteristic
294C42#12411yescharacteristic
295C42#12611yescharacteristic
296C42#12611yescharacteristic
297C23—41no—
298C23—41no—
299C23#38011yescharacteristic
300C23#38611yescharacteristic
301C23#39011yescharacteristic
302C23#41612yes—
303C23#41912yes—
304Q8—44no—
305Q8—44no—
306Q8—82no—
307Q8—82no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—44no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—82no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4#38511yescharacteristic
331C2×C4#38511yescharacteristic
332C2×C4#38811yescharacteristic
333C2×C4#38811yescharacteristic
334C2×C4#39211yescharacteristic
335C2×C4#39311yescharacteristic
336C2×C4#39411yescharacteristic
337C2×C4#39411yescharacteristic
338C2×C4#39611yescharacteristic
339C2×C4#39611yescharacteristic
340C2×C4#39711yescharacteristic
341C2×C4#39911yescharacteristic
342C2×C4#45212yes—
343C2×C4#45212yes—
344C2×C4#46412yes—
345C2×C4#46412yes—
346C2×C4#47912yes—
347C2×C4#47912yes—
348C2×C4#48512yes—
349C2×C4#48512yes—
350C2×C4#48812yes—
351C2×C4#49112yes—
352C2×C4#49511yescharacteristic
353C2×C4#49511yescharacteristic
354C2×C4#49711yescharacteristic
355C2×C4#49711yescharacteristic
356C8—82no—
357C8—82no—
358C8—82no—
359C8—82no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—42no—
367C22—42no—
368C22#143911yescharacteristic
369C22#180512yes—
370C22#187312yes—
371C22#195811yescharacteristic
372C22#196011yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—84no—
381C4—82no—
382C4—82no—
383C4—162no—
384C4#186812yes—
385C4#201511yescharacteristic
386C4#201511yescharacteristic
387C4#202612yes—
388C4#207412yes—
389C4#209711yescharacteristic
390C4#209711yescharacteristic
391C2—22no—
392C2—21no—
393C2—22no—
394C2—21no—
395C2#1105211yescharacteristic
396C2#1108811yescharacteristic
397C2#1109411yescharacteristic
subgroupG/H
centerC2×C4#392
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
socleC22#1439
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#213322
#207552
#174862
C2×#14812
#80952
#79242
#78932